Processing methods based on fuzzy criteria have become established in recent years because of their capacity to provide solutions for a wide range of control problems by overcoming the intrinsic drawbacks of conventional methods, for example those based on Boolean logic.
This is demonstrated by the extensive literature, including patent documents, relating to these methods.
For example, EP-A-0 675 431 describes a method, usable with an electronic controller operating with logical procedures of the fuzzy type, for storing membership functions of logical variables defined within what is called a discourse universe discretized at a finite number of points. The method stores triangular or trapezoidal membership functions by means of memory words, each comprising a first portion containing an encoding of the vertex of the membership function, a second portion containing an encoding corresponding to the slope of at least one side of the membership function, and a third portion containing an encoding corresponding to the slope of at least one other side of the function.
EP-A-0 684 549 describes a method for parallel processing of a plurality of inference rules organized in fuzzy sets or logical functions of multiple fuzzy sets comprising membership functions defined in a corresponding discourse universe. The inference rules in question are essentially rules of the IF-THEN type with at least one antecedent (preposition) and at least one consequent (implication). Each antecedent comprises at least one term of comparison between membership functions and a plurality of input data, with each term separated by logical operators. The method comprises at least one step of calculating the weight of each term of the antecedent of each fuzzy logic inference rule as the maximum value of the intersection between the set of input data and the corresponding membership functions.
It is also known that fuzzy logics are very suitable for implementation in the form of integrated circuits. In relation to this, it will be useful to refer to the paper by H. Watanabe et al., “A VLSI Fuzzy Logic Controller with Reconfigurable, Cascadable Architecture,” published in the IEEE Journal of Solid-State Circuits, vol. 25, no. 2, April 1990, pages 376-381. In particular, this paper describes an inference engine based on a fuzzy logic implemented in CMOS technology.
To summarize (for a more detailed description, reference should be made to the documents cited above), the following elements are essentially present in fuzzy processing:
an input variable,
a fuzzy set of the input variable,
membership functions contained in the fuzzy sets,
logical operators (AND and OR) of the fuzzy type, and
a consequent.
As mentioned above in relation to the document EP-A-0 684 549, the fuzzy inference or fuzzy rule used in the fuzzy computation is generally of the type:
IF antecedent THEN consequent
where the antecedent part can generally be expanded into an expression of the type
ing0 is/not_is MFO and/or ing1 is/not_is MF1 . . . and/or ingn is/not_is MF_n.
Therefore, the generic fuzzy rule, such as that shown above, consists of an antecedent made up of atomic conditions (such as “ing0 is/not_is MFO,” which can be denoted for the sake of brevity simply as “V is/not_is M”) related in logical connection by operators such as AND, OR.
The atomic condition expresses the degree to which one element of the discourse universe has membership of a particular fuzzy subset of this universe. The element in question is denoted by the input variable V and the fuzzy subset is characterized by the membership function M.
Additionally, the fuzzy rule is encoded and stored within the structure which is to compute it.
All the methods of storing the fuzzy inference and the corresponding knowledge base associate each input (in a way similar to the procedure used in fuzzy theory) with the set of which it is a member, in other words the corresponding knowledge base which contains all the memberships used by the input variable.
For calculating the fuzzy inference by means of a structure capable of computing it, the discourse universe of the membership functions of all the input variables is translated into a base discourse universe in such a way that the fuzzy inference can be computed. In the case of a calculation structure of the numerical type, the base discourse universe for all the membership functions will be mapped on to a discrete set which extends from 0 to 2n−1, where n is the number of bits specified as the size for all the input variables.